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Chapter 11 Practice Problems 1) If a p-value is statistically significant, this means that: A. It's likely that this result occurred as a result of random variation B. It's unlikely that this result occurred as a result of random variation C. Your null hypothesis is correct D. The p-value is equal to the significance level E. The p-value is greater than the significance level 2) Suppose you calculated a p-value of .0417. How would you interpret this value'? A. You can't interpret it without a predetermined significance level. B. The p-value is highly statistically significant. C. The p-value isn't statistically significant. D. The p-value is tending towards statistical significance. E. The p-value is statistically significant. 3) True or False: Higher p-values indicate stronger statistical significance. 4) A researcher is looking for evidence that some people can predict the outcome of a roll of dice. Out of 500 subjects, 3 have results significantly better than random guessing would produce, meaning these 3 subjects had p-values less than .01. What can you conclude? A. The researcher made a mistake. Exactly 5 people out of 500 should've done better than guessing. B. The null hypothesis isn't rejected since the p-value is less than .01. C. The 497 who didn't have results significantly better than random guessing would produce definitely don't know how to predict the outcomes. D. Not much. Using the laws of chance, you'd expect 5 people on average out of 500 to do that much better than guessing. Having 3 people in that range isn't very far from what you'd expect. E. There's enough evidence to say that people can predict the outcome of a roll of dice. I 5) A researcher believes a population of fish has a normal distribution with a mean weight of 3.4 kilograms and a standard deviation of .8 kilograms. She takes a simple random sample of 30 fish and finds that the mean is 3 kilograms. What's the p-value for a sample mean of 3 or less? (Hint: Remember to use the distribution of x .) A. .0062 B. .009 C. .0041 D. .0051 E. .0031 6) A researcher thinks a population of fish has a mean weight of 3.4 kilograms and a standard deviation of .8 kilograms. She takes a simple random sample of 30 fish and finds that the mean is 3 kilograms. 1 True or False: Using a significance level of .005, there's significant evidence that the population mean is actually lower than 3.4 kilograms. 7) You want to conduct a one sided test of H0 at = .01. What is the critical z value for this test? A. 2.58 B. 2.33 C. 1.96 D. 1.65 E. Not enough information to answer 8) A significance test allows you to reject H0 at the .05 level of significance. Which of the following are true? I. You can reject H0 at the .01 level of significance II. Ha can be rejected at the .05 level of significance III. H0 can be rejected at the .10 level of significance A. B. C. D. E. I only II only III only I and II only II and III only 9) Suppose we have a hypothesized population mean = 50, and we use our sample data to construct a 98% confidence interval (48, 54). Which of the statements is true if our Ha is 50? A. We can reject the null hypothesis at = .05. B. We can't reject the null hypothesis at = .05. C. We can reject the null hypothesis at = .02. D. We can't reject the null hypothesis at = .02. E. We can't reject the null hypothesis at = .1. 10) A manufacturer claims Fertilizer X will cover an average of 2,000 square feet per bag, with a standard deviation of 250 square feet. A sample of 80 bags was tested and the mean coverage was 2,050 square feet. Using a 95% confidence interval, which of the following would be an acceptable conclusion? A. Reject the null that the mean is 2000 B. Reject the null that the mean is 2000 at = .05 C. Don't reject the null that the mean is 2000 D. Don't reject the null that the mean is 2000 at = .01 E. Reject the null that the mean is 2000 at = .01 11) A manufacturer of parking lot sealant claims its product will cover, on average, 1900 square feet per drum with a standard deviation of 250 square feet. You draw an SRS of 50 drums and find the mean coverage of 1800 square feet. Which of the following two methods will lead you to the same conclusion regarding whether to reject the null? 2 A. B. C. D. E. a) A one sided significance test at a) A two sided significance test at a) A two sided significance test at a) A one sided significance test at a) A one sided significance test at = .05; b) a 95% CI = .05; b) a 95% CI = .01; b) a 95% CI = .01; b) a 90% CI = .01; b) a 99% CI 12) A fisheries report states that the average length of a population of adult fish is 26 inches, with a standard deviation of 6 inches. Katie draws a sample of 45 fish at random and finds the average length is 24.5 inches. She wants to know whether the true mean length is 26 inches at a significance level of = .01. If he were to use a confidence interval that would give the same result as a two sided significance test at = .01, what would she use for a critical z value? A. z* = 1.96 B. z* = 2.33 C. z* = 1.64 D. z* = .95 E. z* = 2.58 Questions 13-14 refer to the scenario below: An advertisement claims HairBuilder cures male pattern baldness. Your father wouldn't mind having more hair and is evaluating the advertisement's claim. 13) If your father makes a Type I error in his evaluation, which of the following will be true? A. The cure really works, but your father doesn't believe the claim and doesn't buy the medication. B. The cure really works, and your father believes the claim and buys the medication. C. The cure doesn't work, but your father believes the claim and buys the medication. D. The cure doesn't work, and your father doesn't believe the claim and doesn't buy the medication. E. None of these will be true. You must have a specific alternative in order to determine the risks of a Type I error. 14) If your father makes a Type II error in his evaluation, which of the following will be true? A. The cure really works, but your father doesn't believe the claim and doesn't buy the medication. B. The cure really works, and your father believes the claim and buys the medication. C. The cure doesn't work, but your father believes the claim and buys the medication. D. The cure doesn't work, and your father doesn't believe the claim and doesn't buy the medication. E. None of these will be true. You must have a specific alternative in order to determine the risks of a Type II error. 15) Which of the following best describes the power of a test? A. It's the probability that you mistakenly accept a false hypothesis. 3 B. It's the probability that you correctly accept a true hypothesis. C. It's the probability that you mistakenly accept a false hypothesis. D. It's the probability that a test will successfully reject a false hypothesis. E. It's the probability that you mistakenly reject a true hypothesis. 16) A market claims the average weight of a package of hamburger in its meat department is one pound, with a standard deviation of .18 1b. A manager decides to test H0 : = 1 against the two-sided alternative Ha: 1. It decides to reject Ho if a sample of 35 packages differs from 1 by more than 1.5 standard deviations. What's the probability of a Type 1 error? (Hint: Use your calculator.) A. .87 B. .05 C. .13 D. .067 E. You can't determine the probability of a Type I error unless you know the significance level of the test. 17) A market claims the average weight of a package of hamburger in its meat department is one pound, with a standard deviation of .18 lb. A manager decides to test H0 : = 1 against the one-sided alternative Ha: u < 1 at the .01 level of significance. To do this, he randomly selects 35 packages of meat. For what range of values of x would you reject the null hypothesis? A. x > 1.07 B. x < .9226 C. x < .93 or x > 1.07 D. x < 1.07 E. x < .93 18) A market claims the average weight of a package of hamburger in its meat department is one pound, with a standard deviation of .181b. A manager decides to test H0: = 1 against the one-sided alternative Ha: < 1 at the .0 1 level of significance by weighing a sample of 35 packages of hamburger. The manager will reject the null hypothesis if x < .93. Suppose the mean weight of all hamburger packages is really .9 lb. Find the probability of a Type II error and the power of the test. A. .01, .99 B. .16, .84 C. .43, .56 D. .84, .16 I E. .56, .43 19) Which of the following are true statements? I. The p-value of a test is the probability of obtaining a result as extrreme as the one obtained assuming the null hypothesis is true. II. If the p-value for a test is .015, the probability that the null hypothesis is true is .015. III. When the null hypothesis is rejected, it is because it is not true. 4 A. B. C. D. E. I only II only III only I and III None of the above gives the complete set of true responses. 20) A coffee-dispensing machine is supposed to deliver 8 ounces of liquid into each paper cup, but a consumer believes that the actual amount is less. As a test, he plans to obtain a sample of 36 cups of the dispensed liquid and, if the mean content is less than 7.75 ounces, to reject the 8ounce claim. If the machine operates with a standard deviation of 0.9 ounces, what is the probability that the consumer will mistakenly reject the 8-ounce claim even though the claim is true? A. .0475 B. .0950 C. .1500 D. .3897 E. .4525 21) Which of the following are true statements? I. Test of significance (hypothesis tests) are designed to measure the strength of evidence against the null hypothesis. II. A well-planned test of significance should result in a statement either that the null hypothesis is true or that it is false. III. The alternative hypothesis is one-sided if there is interest in deviations from the null hypothesis in only one direction. A. I and II B. I and III C. II and III D. I, II, and III E. None of the above gives the complete set of true responses. 22) A government statistician claims that the mean monthly rainfall along the Liberian coast is 15.0 inches with a standard deviation of 12.0 inches. A meterologist plans to test this claim with measurements over 3.5 years (42 months). If she finds a sample mean more than 2.0 inches different from the claimed 15.0 inches, she will reject the government statistician’s claim. What is the probability that the meterologist will mistakenly reject a true claim? A. .0675 B. .1401 C. .2802 D. .4325 E. .8650 23) Which of the following are true statements? I. The alternative hypothesis is stated in terms of a sample statistic. II. A large p-value indicates strong evidence against the null hypothesis. III. If a sample is large enough, the necessity for it to be a simple random sample is diminished. A. I only B. II only C. III only D. Exactly two of the above statements are true. 5 E. None of the above statements are true. 24) An automotive company executive claims that a mean of 48.3 cars per dealership are being sold each month. A major stockholder believes this claim is high and runs a test by sampling 30 dealerships. What conclusion is reached if the sample mean is 45.4 cars with a standard deviation of 15.4? A. There is sufficient evidence to prove the executive’s claim is true. B. There is sufficient evidence to prove the executive’s claim is false. C. The stockholder has sufficient evidence to reject the executive’s claim. D. The stockholder does not have sufficient evidence to reject the executive’s claim. E. There is not sufficient data to reach any conclusion. 25) A pharmaceutical company claims that a medication will produce a desired effect for a mean time of 58.4 minutes. A government researcher runs a hypothesis test of 250 patients and calculates a mean of x-bar = 59.5 with a standard deviation of s = 8.3. In which of the following intervals is the p-value located? A. p < .01 B. .01 < p < .025 C. .025 < p < .05 D. .05 < p < .10 E. p > .10 6